Even in the largest telescopes, nearly all stars are just points. The surfaces of stars can be visualized
by indirect methods only. Magnetic fields on the surface reveal their presence through the Zeeman effect
in the spectrum of a star. Spectral lines are split into several components, and the width of the splitting
is a measure for the strength of the magnetic field. The rotation of the star causes a Doppler effect:
the spectral lines are shifted slightly to the blue for structures on one side of the star while
structures on the other side cause red-shifted lines. The combination of the two effect allows us to
determine the surface distribution of the stellar magnetic field. If spectra of different light polarisations
are taken form the star, even the direction of the magnetic field vectors can be reproduced (from what is
called Stokes parameters).

Stellar spectra with very high resolution are necessary for the reconstruction of the stellar surface. We
used the SOFIN spectrograph at the Nordic Optical Telescope on La Palma with a resolution of up to 170000.
The analysis of the spectra is made with a Zeeman-Doppler imaging (ZDI) inversion code
iMap which reconstructs the
best-matching distribution of magnetic fields on the stellar surface from the spectral line profiles.
In a first application we have applied our code to spectropolarimetric observation of the K1 subgiant star
II Peg. The data (Stokes I and Stokes V) were collected in an observing campaign in 2004 and cover a whole
rotational period of the star. Prior to the actual Zeeman-Doppler inversion we have used our code in
Doppler imaging mode to retrieve the temperature distribution of the surface of II Peg, where we have used the
Ca I 6439Å line. This information was subsequently used in the ZDI inversion to determine the magnetic
field from the phase resolved Stokes V profiles of the Fe I 5497Å line,

We also notice only a small correlation between the dark and cool starspots as retrieved by our Doppler imaging run and the
magnetic field distribution from the ZDI. This seems to be plausible because of the strong suppression of the photon
flux in the spot regions which are between 700K and 1000K cooler than the quiet and hot parts of the surface.

The achievements in inversion techniques for stellar surfaces are particularly interesting for the
next-generation spectropolarimeter PEPSI which
will be installed at the Large Binocular Telescope (LBT) in
Arizona in 2009. Among various other tasks, PEPSI will be able to provide data for the reconstruction of surface
magnetic fields of a very large sample of active cool stars.

Temperature map (left) and surface magnetic field map (right) of II Pegasi. The "needles" in the right image indicate
the field vector for each surface pixel, the color represents the absolute field strength.

Mercator maps of the azimuthal (top), meridional (middle), and radial (bottom) field strength.